scholarly journals Accretion of Planetesimals within a Gaseous Ring

1980 ◽  
Vol 33 (3) ◽  
pp. 623 ◽  
Author(s):  
AJR Prentice
Keyword(s):  
Numerical Study ◽  
Nonlinear Effects ◽  
Equation Of Motion ◽  
The Sun ◽  
Gas Density ◽  
Planetary Embryo ◽  
Outer Atmosphere ◽  
Gravitational Influence ◽  
High Reynolds ◽  
Gas Drag

An analytical study is made of the accretion of planetesimals by a planetary embryo within the framework of a modem Laplacian theory for the formation of the planetary system. The equation of motion of the particle, which is initially comoving ahead of (or behind) the growing planet on the same circular Keplerian orbit about the Sun, is examined both in the presence and abseflce of a gaseous torus which is also centred on the same mean orbit. The gas density in the torus is taken to be uniform and the drag exerted on the particle is assumed to vary as the square of the relative velocity, corresponding to motion at high Reynolds number. It is found that the gas acts as a damper to the coriolis acceleration due to the Sun in the rotating frame of reference of the embryo, which tends to pull the particle off the mean circular orbit, thus preventing accretion. In the absence of the gaseous drag, less than 1 % of particles lying well inside the so-called sphere of gravitational influence of the embryo are accreted, whilst if the gas drag is included nearly all of these particles are captured. In all instances the accreting particles impart a spin angular momentum to the embryo which is prograde with the orbital motion. The actual spin rate decreases with increasing gas drag and is found to be lowest for the innermost planets Mercury and Venus, where the gas density is greatest. A more detailed numerical study is probably required to determine the rotational period of larger planets and planetary cores which possess an outer atmosphere, not included in the p$ent study, and where nonlinear effects in the particle's equation of motion cannot be ignored.' 'r.'

A numerical study of turbulence under temporally evolving axisymmetric contraction and subsequent relaxation

2016 ◽  
Vol 805 ◽  
pp. 460-493 ◽  
Author(s):  
M. P. Clay ◽  
P. K. Yeung
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Numerical Study ◽  
Nonlinear Effects ◽  
Spectral Evolution ◽  
One Dimensional ◽  
Contraction Ratio ◽  
Wide Range ◽  
Small Scales ◽  
High Reynolds

Direct numerical simulations using up to $4096^{3}$ grid points on a deforming domain have been used to study the response of initially isotropic turbulence to a period of spatially uniform axisymmetric contraction (with one extensional and two equally compressive directions) and subsequent relaxation. A time-dependent strain rate is formulated to closely correspond to the downstream evolution in the wind tunnel experiments of Ayyalasomayajula & Warhaft (J. Fluid Mech., vol. 566, 2006, pp. 273–307), with a smoothly varying 4 : 1 contraction ratio. The application of strain leads to anisotropy in both the large scales and the small scales, in a manner where nonlinear effects not considered in rapid-distortion theory play an important role. Upon termination of strain, the small scales quickly return to isotropy while a residual level of anisotropy appears to persist at the large scales. The simulations are shown to reproduce many key findings from experiments, including distinctive changes in the form of the one-dimensional spectra in the extensional direction that arise at sufficiently high Reynolds number, during both the straining and relaxation periods. Scale-dependent measures of anisotropy are presented in terms of one-dimensional spectra and axisymmetric versions of the energy spectrum. To explain the observed changes in spectral shapes, various terms in the spectral evolution equation representing rapid pressure strain, slow pressure strain, production, nonlinear transfer and viscous dissipation are computed, showing that nonlinear effects take a dominant role when a wide range of scales exists. In particular, the ‘double-peak’ spectral form observed in experiments at high Reynolds number is found to be a consequence of the small scales relaxing towards isotropy much faster than the large scales. A comparison of results obtained from computational domains of varying sizes and grid resolutions show that the numerical findings are robust.

The Interpretation of Solar Spectral Intensities

1988 ◽  
Vol 102 ◽  
pp. 329
Author(s):  
R.W.P. McWhirter
Keyword(s):  
Emission Measure ◽  
Physical Nature ◽  
Atomic Data ◽  
The Sun ◽  
Atomic Properties ◽  
Outer Atmosphere ◽  
Spectral Intensities ◽  
Thin Plasma ◽  
Number Of Authors

The intensity of a specrtal line from an optically thin plasma such as the outer atmosphere of the sun depends on both the atomic properties of the atomic ion responsible for the line and the physical nature of the plasma. In this paper we discuss the various ways in which the measured spectral intensities from the sun are used to discover something about the nature of the sun’s atmosphere. The technique has been referred to as the emission measure method. It has important limitations in terms of the accuracy of the specrtal data as well as the atomic data. We discuss some of these and suggest methods by which they may be assessed. The technique is illustrated by application to real observations from a number of authors.

Finite difference code for velocity and surface traction of a Fluid between Two Eccentric Spheres

2015 ◽  
Vol 11 (1) ◽  
pp. 2960-2971
Author(s):  
M.Abdel Wahab
Keyword(s):  
Velocity Field ◽  
Angular Velocity ◽  
Finite Difference ◽  
Numerical Study ◽  
Outer Sphere ◽  
Equation Of Motion ◽  
Annular Region ◽  
Surface Traction ◽  
Angular Velocities ◽  
Axis Passing

The Numerical study of the flow of a fluid in the annular region between two eccentric sphere susing PHP Code isinvestigated. This flow is created by considering the inner sphere to rotate with angular velocity 1  and the outer sphererotate with angular velocity 2  about the axis passing through their centers, the z-axis, using the three dimensionalBispherical coordinates (, ,) .The velocity field of fluid is determined by solving equation of motion using PHP Codeat different cases of angular velocities of inner and outer sphere. Also Finite difference code is used to calculate surfacetractions at outer sphere.

An Experimental and Numerical Study of Heat Transfer and Pressure Loss in a Rectangular Channel With V-Shaped Ribs

2006 ◽  
Author(s):  
Michael Maurer ◽  
Jens von Wolfersdorf ◽  
Michael Gritsch
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Enhancement ◽  
Thermal Performance ◽  
Pressure Loss ◽  
Numerical Study ◽  
Rectangular Channel ◽  
Reynolds Numbers ◽  
Transfer Enhancement ◽  
High Reynolds Numbers ◽  
High Reynolds

An experimental and numerical study was conducted to determine the thermal performance of V-shaped ribs in a rectangular channel with an aspect ratio of 2:1. Local heat transfer coefficients were measured using the steady state thermochromic liquid crystal technique. Periodic pressure losses were obtained with pressure taps along the smooth channel sidewall. Reynolds numbers from 95,000 to 500,000 were investigated with V-shaped ribs located on one side or on both sides of the test channel. The rib height-to-hydraulic diameter ratios (e/Dh) were 0.0625 and 0.02, and the rib pitch-to-height ratio (P/e) was 10. In addition, all test cases were investigated numerically. The commercial software FLUENT™ was used with a two-layer k-ε turbulence model. Numerically and experimentally obtained data were compared. It was determined that the heat transfer enhancement based on the heat transfer of a smooth wall levels off for Reynolds numbers over 200,000. The introduction of a second ribbed sidewall slightly increased the heat transfer enhancement whereas the pressure penalty was approximately doubled. Diminishing the rib height at high Reynolds numbers had the disadvantage of a slightly decreased heat transfer enhancement, but benefits in a significantly reduced pressure loss. At high Reynolds numbers small-scale ribs in a one-sided ribbed channel were shown to have the best thermal performance.

Numerical Study of Viscous Flows Inside Partially Filled Spinning and Coning Cylinders

1996 ◽  
Vol 118 (2) ◽  
pp. 335-340 ◽  
Author(s):  
Mohamed Selmi
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Center Of Mass ◽  
Steady Motion ◽  
Practical Interest ◽  
Nonlinear Effects ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Practical Applications ◽  
Analysis And Design

This paper is concerned with the solution of the 3-D-Navier-Stokes equations describing the steady motion of a viscous fluid inside a partially filled spinning and coning cylinder. The cylinder contains either a single fluid of volume less than that of the cylinder or a central rod and a single fluid of combined volume (volume of the rod plus volume of the fluid) equal to that of the cylinder. The cylinder rotates about its axis at the spin rate ω and rotates about an axis that passes through its center of mass at the coning rate Ω. In practical applications, as in the analysis and design of liquid-filled projectiles, the parameter ε = τ sin θ, where τ = Ω/ω and θ is the angle between spin axis and coning axis, is small. As a result, linearization of the Navier-Stokes equations with this parameter is possible. Here, the full and linearized Navier-Stokes equations are solved by a spectral collocation method to investigate the nonlinear effects on the moments caused by the motion of the fluid inside the cylinder. In this regard, it has been found that nonlinear effects are negligible for τ ≈ 0.1, which is of practical interest to the design of liquid-filled projectiles, and the solution of the linearized Navier-Stokes equations is adequate for such a case. However, as τ increases, nonlinear effects increase, and become significant as ε surpasses about 0.1. In such a case, the nonlinear problem must be solved. Complete details on how to solve such a problem is presented.

scholarly journals Numerical Analysis of Fluid Flow on Wall Cylinder Circular with K-ε Modeling for a High Reynolds Rate

2019 ◽  
Vol 1 (3) ◽  
pp. 43-50
Author(s):  
M. Yasep Setiawan ◽  
Wawan Purwanto ◽  
Wanda Afnison ◽  
Nuzul Hidayat
Keyword(s):  
Fluid Flow ◽  
Numerical Study ◽  
General Procedure ◽  
Circular Cylinders ◽  
Cylinder Wall ◽  
Two Dimensional ◽  
Third Order ◽  
Physical Information ◽  
Flow Through ◽  
High Reynolds

This study discusses the numerical study of two-dimensional analysis of flow through circular cylinders. The original physical information entered in the equation governing most of the modeling is transferred into a numerical solution. Fluid flow on two-dimensional circular cylinder wall using high Reynolds k-ε modeling (Re = 106), Here we will do 3 modeling first oder upwind, second order upwind and third order MUSCL by using k-ε standard.  The general procedure for this research is formulated in detail for allocations in the dynamic analysis of fluid computing. The results of this study suggest that MUSCL's third order modeling gives more accurate results better than other models.

A NUMERICAL STUDY OF FLUID INJECTION AND MIXING UNDER NEAR-CRITICAL CONDITIONS

2012 ◽  
Vol 19 ◽  
pp. 39-49 ◽  
Author(s):  
HUA-GUANG LI ◽  
XI-YUN LU ◽  
VIGOR YANG
Keyword(s):  
Reynolds Number ◽  
Shear Layer ◽  
Numerical Study ◽  
Ideal Gas ◽  
Critical Conditions ◽  
Reference Case ◽  
Nitrogen Injection ◽  
Volume Dilatation ◽  
High Reynolds ◽  
The Ideal

Nitrogen injection under conditions in close vicinity of liquid-gas critical point is studied through numerical simulation. The thermodynamic and transport properties of fluid exhibit anomalies in the near-critical fluid regime. These anomalies can cause distinctive effects on heat transfer and hydrodynamics. To focus on the influence of the highly variable properties and avoid the difficulties encountered in modeling high Reynolds number flows, a relatively low injection Reynolds number is adopted. A reference case with the same configuration and Reynolds number is also simulated in the ideal gas regime. Full conservation laws, real-fluid thermodynamic and transport phenomena are accommodated in the model. The obtained results reveal that the flow features of the near-critical fluid jet are significantly different from the ideal gas case. The near-critical fluid jet spreads faster and mixes better with the ambient fluid compared to the ideal gas jet. It is also identified that vortex pairing process develops faster in the near-critical case than in the ideal gas case. Detailed analysis of data at different streamwise positions including both flat shear layer region and fully developed vortex region reveals the effect of volume dilatation and baroclinic torque plays an important role in the near-critical fluid case. The volume dilatation effect disturbs the shear layer and makes it more unstable. The volume dilatation and baroclinic effects strengthen the vorticity and stimulate the vortex rolling up and pairing process.

scholarly journals The transformation of an interfacial solitary wave of elevation at a bottom step

2009 ◽  
Vol 16 (1) ◽  
pp. 33-42 ◽  
Author(s):  
V. Maderich ◽  
T. Talipova ◽  
R. Grimshaw ◽  
E. Pelinovsky ◽  
B. H. Choi ◽  
...  
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Numerical Study ◽  
Nonlinear Effects ◽  
Ocean Model ◽  
Gardner Equation ◽  
Fully Nonlinear ◽  
Layer Flow ◽  
The One ◽  
Bottom Step

Abstract. In this paper we study the transformation of an internal solitary wave at a bottom step in the framework of two-layer flow, for the case when the interface lies close to the bottom, and so the solitary waves are elevation waves. The outcome is the formation of solitary waves and dispersive wave trains in both the reflected and transmitted fields. We use a two-pronged approach, based on numerical simulations of the fully nonlinear equations using a version of the Princeton Ocean Model on the one hand, and a theoretical and numerical study of the Gardner equation on the other hand. In the numerical experiments, the ratio of the initial wave amplitude to the layer thickness is varied up one-half, and nonlinear effects are then essential. In general, the characteristics of the generated solitary waves obtained in the fully nonlinear simulations are in reasonable agreement with the predictions of our theoretical model, which is based on matching linear shallow-water theory in the vicinity of a step with solutions of the Gardner equation for waves far from the step.

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